Question: $\begin{cases}a(1)=20\\\\ a(n)=a(n-1)\cdot\dfrac32 \end{cases}$ What is the $3^{\text{rd}}$ term in the sequence?
Explanation: This is a recursive formula. It tells us that the first term is $20$ and that the common ratio is $\dfrac32$. $\begin{aligned} {a(1)}&=20 \\\\ {a(2)}&={a(1)}\cdot\dfrac32=30 \\\\ {a(3)}&={a(2)}\cdot\dfrac32=45 \end{aligned}$ The $3^\text{rd}$ term is $45$.